Best Known (27, 53, s)-Nets in Base 32
(27, 53, 196)-Net over F32 — Constructive and digital
Digital (27, 53, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 20, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 33, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 20, 98)-net over F32, using
(27, 53, 288)-Net in Base 32 — Constructive
(27, 53, 288)-net in base 32, using
- 10 times m-reduction [i] based on (27, 63, 288)-net in base 32, using
- base change [i] based on digital (9, 45, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 45, 288)-net over F128, using
(27, 53, 566)-Net over F32 — Digital
Digital (27, 53, 566)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3253, 566, F32, 26) (dual of [566, 513, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3253, 1032, F32, 26) (dual of [1032, 979, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3251, 1024, F32, 26) (dual of [1024, 973, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3245, 1024, F32, 23) (dual of [1024, 979, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3253, 1032, F32, 26) (dual of [1032, 979, 27]-code), using
(27, 53, 250273)-Net in Base 32 — Upper bound on s
There is no (27, 53, 250274)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 59 288582 122350 118508 818677 020112 873620 911583 350592 285475 111214 922628 825344 891448 > 3253 [i]